Craven: Bridging Algebra and Geometry with n-gram Proofs
Joshua D. Craven, a recent Master of Education student and now an Adjunct Professor in Mathematics Education, published an article on “Bridging Algebra and Geometry with n-gram Proofs” in the May 2010 issue of Mathematics Teacher. Craven is a National Board Certified mathematics teacher at Perkiomen Valley High School in Collegeville, Pa. He uses mathematics education as a vehicle to teach students to think using higher-level reasoning skills.
“With the help of hint cards, students formulate and prove conjectures about angle measures, first for pentagrams and then for hexagrams and general n-grams,” he writes. “For many students, geometry is the first course in which mathematical proof takes center stage. I try to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Some of my more effective activities are those scaffolded to lead students through tasks that require increasingly sophisticated mathematical reasoning and proof.” Read the article.